Thanks to both for your answers and especially to amgepo for the confirmation that doesn't cause problems even when repeatedly used.

I would assume not. The Caller simply refers to the function in the Callee. So long as the function name is the same in the Callee, it's contents are loaded WHEN the Caller calls the function, so a recompile would not be needed.
This actually depends on how the function is refered to, it does not have to be by the name. And if I remember correctly the last time I looked at a pex file, it was not by name.

If it has been an index or an address offset, for example, adding a new function would likely mess it up. Fortunately Beth apparently used something else (hashcode?) or they have been smart with their indices.